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LES verification of Kolmogorov closure for effective dissipation of the turbulent flux of momentum

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Budget equation for the vertical turbulent flux of potential temperature The “pressure term” is shown to be proportional to the mean squared fluctuation of potential temperature On the r.h.s. of the equation, the 1 st term (generating positive heat flux) counteracts to the 2 nd term (generating negative heat flux) and assures self-preservation of turbulence in very stable stratification

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Relaxation equation for dissipation time scale Evolution of t T is controlled by the tendency towards equilibrium: and distortion by non-stationary processes and, in heterogeneous flows, by the mean-flow and turbulent transports. Their counteraction is described by the RELAXATION EQUATION: where is the relaxation constant.

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 TKE budget equation is INSUFFICIENT E K and E P are equally important  Е = E K + E P  There is no Ri c in the energetic sense; experimental data confirm this theoretical conclusion up to Ri ~ 10 2  There is a threshold Ri ~ 0.2-0.3 (quite close to the liner instability limit) – separating principally different regimes of “strong” and “weak“ turbulence  The newly discovered “weak turbulence regime” is typical of the free atmosphere and deep ocean, wherein it determines turbulent transport of the energy and momentum and diffusion of passive scalars  A hierarchy of EFB closure models – new instruments for research and modelling applications Conclusions